How can I restore my iphone 5c to factory settings?

A few months ago my daughter lost her iPhone 5c in the woods. We had it deactivated after that. Just a few days ago, we found it again - someone had found it right away and it was safe and unharmed. We have been trying to reactivate it, but it keeps asking for my daughter's Apple ID and password. She just changed them, but it doesn't want the current ID/password, it wants the old one that she doesn't remember. Is there a way we can reset the phone to its factory settings and wipe out all the old information? I notice there is a tiny pinhole on the side of the phone - can we do it by depressing that? I'd hate to throw away a $300 phone, so we're trying everything we can.